A051774 Contracted numbers.

6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 78, 80, 84, 88, 90, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 140, 144, 150, 154, 156, 160, 162, 165, 168, 170, 174, 175, 176, 180, 182, 186

Offset: 1

Author

Alexander Benjamin Schwartz (QBOB(AT)aol.com), Dec 08 1999

Keywords

• nonn

Comments

n is said to be contracted if and only if n has distinct divisors d_1 < d_2 < ... < d_k such that d_1+d_2+...+d_(k-1) >= d_k. Note that d_k need not be the greatest divisor of n -- see the examples.

Examples

			6 has divisors 1, 2, 3, 6, and 1+2 >= 3, so 6 is a member. 45 has divisors 1, 3, 5, 9, 15, 45, and 1+3+5+9 = 18 > 15, so 45 is a member. - _N. J. A. Sloane_, Jun 12 2021
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Numbers not in A051772.

Programs

Mathematica

cnQ[n_]:=Module[{d=Divisors[n],len},len=Length[d];AnyTrue[Table[Take[ d,k],{k,3,len}],Total[Most[#]]>=Last[#]&]]; Select[Range[200],cnQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 12 2021 *)